Resonance/energy levels contributing structures

In summary, Robert B. Grossman discusses resonance in the context of the Schrodinger equation. He defines it as a degenerate solution of equal energy, and explains that it is not limited to structures of the same energy. The concepts should be exposed in books by Linus Pauling or Eyring Walter and Kimball.
  • #1
DDTea
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I'm working my way through The Art of Writing Reasonable Organic Reaction Mechanisms by Robert B. Grossman (excellent book, by the way), but the way he describes resonance is confusing me. I feel like the more I think about it, the more confusing it gets.

Consider a carbon-carbon double bond: C=C. He says that there are a few different ways that the pi electrons can be distributed in this bond:

C=C
(-)C--C(+)
(+)C--C(-)
.C--C.

Where the last structure is a radical. Although some of those structures are theoretically possible, they would offer a poor description of the behavior of the C=C . So, he develops a set of rules for which theoretical contributing structures are higher in energy and thus poorer descriptions of the chemical behavior.

So my question is, is this definition of "higher energy" a literal definition? Or am I misunderstanding the definition of resonance: degenerate solutions for the energy term in the Schrodinger equation--i.e., of equal energy!
 
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  • #2
If he is using an isolated double bond to describe resonance it is only being used in the form of an object lesson. ie. you might draw a double bond in the following ways...
just as you might draw resonance structures in the following ways. How the energies of the various representations are calculated, if not discussed by Grossman, can be assumed to be by one of the various MO methods that are accurate enough to provide a relative ranking.
 
  • #3
The different structures correspond best to a set of valence bond structures. You can now form a matrix representaiton of your molecular hamiltonian using these structures as a basis. The diagonal matrix elements will be the "energies" of the hypothetical isolated structures. The importance of a given structure in the real wavefunction of the molecule depends not only on tihs energy but also on the value of the non-diagonal matrix elements. However it is important that resonance is not restricted to structures of the same energy.
These concepts should be exposed in the books by Linus Pauling, or, on a more theoretical basis in the classic book "quantum chemistry" by Eyring Walter and Kimball.
 

1. What is resonance in chemistry?

Resonance in chemistry refers to the concept of multiple valid Lewis structures that can be drawn for a molecule or ion. This is due to the delocalization of electrons within the molecule or ion, resulting in a more stable overall structure.

2. How do resonance structures affect the stability of a molecule?

Resonance structures contribute to the stability of a molecule by distributing electrons across multiple atoms, resulting in a more even distribution of charge. This reduces the overall energy of the molecule, making it more stable.

3. How do energy levels contribute to resonance?

The energy levels of an atom determine the location of its valence electrons. When a molecule has multiple resonance structures, the energy levels of the atoms involved play a crucial role in determining which structure is more stable.

4. Can all molecules exhibit resonance?

No, not all molecules can exhibit resonance. Only molecules with delocalized electrons, such as those with double bonds, lone pairs, or conjugated systems, can exhibit resonance.

5. What is the difference between a contributing structure and a resonance hybrid?

A contributing structure is a valid Lewis structure that contributes to the overall resonance hybrid of a molecule. The resonance hybrid is a combination of all the contributing structures, representing the true structure of the molecule.

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